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algebra word problem

During a research experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 7:00am there were 6,000 bacteria present in the culture. At noon, the number of bacteria grew to 6,700. How many bacteria will there be at midnight?

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Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (7 lesson ratings) (7)
If the growth rate is proportional to the population, then it is exponential.  That is the number of bacteria at time t, call it B(t)=B(0)ekt.  In our case we have B(t)=6000ekt.  The k is determined by noting that 12 noon, t=5 we have 6700=6000e5k, and so 5k=ln(6700/6000), or k=.022069611433773. At midnight, t=17 hours we have that
B(17)=6000e.37518339...=6000×1.45525827...=8731.549... or about 8732


In no way does this qualify as an algebra word problem, unless you are simply told about the growth and not asked to show it.
SURENDRA K. | An experienced,patient & hardworking tutorAn experienced,patient & hardworking tut...
At 7am no of bacteria present.       = 6000
At 12 noon no of bacteria present   = 6700
In 5 hours increase in bacteria.       = 6700-6000=700
In one hour increase in bacteria       = 700/5=140
In 12 hours(at mid night) increase in bacteria.      = 140*12=      1680
So, no of bacteria present at midnight. = 6700+1680=8380